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<a class="vector-toc-link" href="#Numărul_de_laturi_ale_unui_poliedru"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Numărul de laturi ale unui poliedru</span> </div> </a> <ul id="toc-Numărul_de_laturi_ale_unui_poliedru-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Legătura_cu_fețele" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Legătura_cu_fețele"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Legătura cu fețele</span> </div> </a> <ul id="toc-Legătura_cu_fețele-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Terminologie_alternativă" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Terminologie_alternativă"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Terminologie alternativă</span> </div> </a> <ul id="toc-Terminologie_alternativă-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relația_cu_muchiile_din_grafuri" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relația_cu_muchiile_din_grafuri"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Relația cu muchiile din grafuri</span> </div> </a> <ul id="toc-Relația_cu_muchiile_din_grafuri-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografie"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Bibliografie</span> </div> </a> <ul id="toc-Bibliografie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lectură_suplimentară" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Lectură_suplimentară"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Lectură suplimentară</span> </div> </a> <ul id="toc-Lectură_suplimentară-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Legături_externe" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Legături_externe"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Legături externe</span> </div> </a> <ul id="toc-Legături_externe-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Cuprins" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Comută cuprinsul" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Comută cuprinsul</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Latură (geometrie)</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Mergeți la un articol în altă limbă. Disponibil în 50 limbi" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-50" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">50 limbi</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AD%D8%A7%D9%81%D8%A9_(%D9%87%D9%86%D8%AF%D8%B3%D8%A9)" title="حافة (هندسة) – arabă" lang="ar" hreflang="ar" data-title="حافة (هندسة)" data-language-autonym="العربية" data-language-local-name="arabă" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/Ari" title="Ari – aymara" lang="ay" hreflang="ay" data-title="Ari" data-language-autonym="Aymar aru" data-language-local-name="aymara" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%B6%DB%8C%D9%84%D8%B9_(%D9%87%D9%86%D8%AF%D8%B3%D9%87)" title="ضیلع (هندسه) – South Azerbaijani" lang="azb" hreflang="azb" data-title="ضیلع (هندسه)" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D1%8A%D0%B1" title="Ръб – bulgară" lang="bg" hreflang="bg" data-title="Ръб" data-language-autonym="Български" data-language-local-name="bulgară" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BE%E0%A6%B9%E0%A7%81_(%E0%A6%9C%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%AE%E0%A6%BF%E0%A6%A4%E0%A6%BF)" title="বাহু (জ্যামিতি) – bengaleză" lang="bn" hreflang="bn" data-title="বাহু (জ্যামিতি)" data-language-autonym="বাংলা" data-language-local-name="bengaleză" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Aresta_(geometria)" title="Aresta (geometria) – catalană" lang="ca" hreflang="ca" data-title="Aresta (geometria)" data-language-autonym="Català" data-language-local-name="catalană" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%84%D8%A7" title="لا – kurdă centrală" lang="ckb" hreflang="ckb" data-title="لا" data-language-autonym="کوردی" data-language-local-name="kurdă centrală" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Strana_(geometrie)" title="Strana (geometrie) – cehă" lang="cs" hreflang="cs" data-title="Strana (geometrie)" data-language-autonym="Čeština" data-language-local-name="cehă" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%90%D1%8F%D0%BA_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8)" title="Аяк (геометри) – ciuvașă" lang="cv" hreflang="cv" data-title="Аяк (геометри)" data-language-autonym="Чӑвашла" data-language-local-name="ciuvașă" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Ymyl" title="Ymyl – galeză" lang="cy" hreflang="cy" data-title="Ymyl" data-language-autonym="Cymraeg" data-language-local-name="galeză" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Edge_(geometry)" title="Edge (geometry) – engleză" lang="en" hreflang="en" data-title="Edge (geometry)" data-language-autonym="English" data-language-local-name="engleză" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Latero" title="Latero – esperanto" lang="eo" hreflang="eo" data-title="Latero" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Arista_(geometr%C3%ADa)" title="Arista (geometría) – spaniolă" lang="es" hreflang="es" data-title="Arista (geometría)" data-language-autonym="Español" data-language-local-name="spaniolă" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Serv" title="Serv – estonă" lang="et" hreflang="et" data-title="Serv" data-language-autonym="Eesti" data-language-local-name="estonă" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Ertz_(geometria)" title="Ertz (geometria) – bască" lang="eu" hreflang="eu" data-title="Ertz (geometria)" data-language-autonym="Euskara" data-language-local-name="bască" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B6%D9%84%D8%B9" title="ضلع – persană" lang="fa" hreflang="fa" data-title="ضلع" data-language-autonym="فارسی" data-language-local-name="persană" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/S%C3%A4rm%C3%A4_(geometria)" title="Särmä (geometria) – finlandeză" lang="fi" hreflang="fi" data-title="Särmä (geometria)" data-language-autonym="Suomi" data-language-local-name="finlandeză" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Ar%C3%AAte_(g%C3%A9om%C3%A9trie)" title="Arête (géométrie) – franceză" lang="fr" hreflang="fr" data-title="Arête (géométrie)" data-language-autonym="Français" data-language-local-name="franceză" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Aresta" title="Aresta – galiciană" lang="gl" hreflang="gl" data-title="Aresta" data-language-autonym="Galego" data-language-local-name="galiciană" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A6%D7%9C%D7%A2_(%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94)" title="צלע (גאומטריה) – ebraică" lang="he" hreflang="he" data-title="צלע (גאומטריה)" data-language-autonym="עברית" data-language-local-name="ebraică" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Brid" title="Brid – croată" lang="hr" hreflang="hr" data-title="Brid" data-language-autonym="Hrvatski" data-language-local-name="croată" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/B%C3%B2" title="Bò – haitiană" lang="ht" hreflang="ht" data-title="Bò" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitiană" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%B8%D5%B2_(%D5%A5%D6%80%D5%AF%D6%80%D5%A1%D5%B9%D5%A1%D6%83%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6)" title="Կող (երկրաչափություն) – armeană" lang="hy" hreflang="hy" data-title="Կող (երկրաչափություն)" data-language-autonym="Հայերեն" data-language-local-name="armeană" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Sisi_(geometri)" title="Sisi (geometri) – indoneziană" lang="id" hreflang="id" data-title="Sisi (geometri)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indoneziană" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Spigolo" title="Spigolo – italiană" lang="it" hreflang="it" data-title="Spigolo" data-language-autonym="Italiano" data-language-local-name="italiană" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%BE%BA" title="辺 – japoneză" lang="ja" hreflang="ja" data-title="辺" data-language-autonym="日本語" data-language-local-name="japoneză" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Iri_(tanzeggit)" title="Iri (tanzeggit) – kabyle" lang="kab" hreflang="kab" data-title="Iri (tanzeggit)" data-language-autonym="Taqbaylit" data-language-local-name="kabyle" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AA%A8%EC%84%9C%EB%A6%AC" title="모서리 – coreeană" lang="ko" hreflang="ko" data-title="모서리" data-language-autonym="한국어" data-language-local-name="coreeană" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Kra%C5%A1tin%C4%97" title="Kraštinė – lituaniană" lang="lt" hreflang="lt" data-title="Kraštinė" data-language-autonym="Lietuvių" data-language-local-name="lituaniană" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/%C5%A0%C4%B7autne" title="Šķautne – letonă" lang="lv" hreflang="lv" data-title="Šķautne" data-language-autonym="Latviešu" data-language-local-name="letonă" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B1_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)" title="Раб (геометрија) – macedoneană" lang="mk" hreflang="mk" data-title="Раб (геометрија)" data-language-autonym="Македонски" data-language-local-name="macedoneană" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Sisi_(geometri)" title="Sisi (geometri) – malaeză" lang="ms" hreflang="ms" data-title="Sisi (geometri)" data-language-autonym="Bahasa Melayu" data-language-local-name="malaeză" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Ribbe" title="Ribbe – neerlandeză" lang="nl" hreflang="nl" data-title="Ribbe" data-language-autonym="Nederlands" data-language-local-name="neerlandeză" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kant_i_geometri" title="Kant i geometri – norvegiană nynorsk" lang="nn" hreflang="nn" data-title="Kant i geometri" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegiană nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kant_(geometri)" title="Kant (geometri) – norvegiană bokmål" lang="nb" hreflang="nb" data-title="Kant (geometri)" data-language-autonym="Norsk bokmål" data-language-local-name="norvegiană bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Kraw%C4%99d%C5%BA_(stereometria)" title="Krawędź (stereometria) – poloneză" lang="pl" hreflang="pl" data-title="Krawędź (stereometria)" data-language-autonym="Polski" data-language-local-name="poloneză" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Aresta" title="Aresta – portugheză" lang="pt" hreflang="pt" data-title="Aresta" data-language-autonym="Português" data-language-local-name="portugheză" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B5%D0%B1%D1%80%D0%BE_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Ребро (геометрия) – rusă" lang="ru" hreflang="ru" data-title="Ребро (геометрия)" data-language-autonym="Русский" data-language-local-name="rusă" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Side" title="Side – Simple English" lang="en-simple" hreflang="en-simple" data-title="Side" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Stranica" title="Stranica – slovenă" lang="sl" hreflang="sl" data-title="Stranica" data-language-autonym="Slovenščina" data-language-local-name="slovenă" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Brinja_(gjeometri)" title="Brinja (gjeometri) – albaneză" lang="sq" hreflang="sq" data-title="Brinja (gjeometri)" data-language-autonym="Shqip" data-language-local-name="albaneză" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kant_(geometri)" 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data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aspect</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mută în bara laterală</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ascunde</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">De la Wikipedia, enciclopedia liberă</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="ro" dir="ltr"><div style="float: right;"><ul class="gallery mw-gallery-traditional" style="max-width: 326px;"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Triangle.TrigArea.svg" class="mw-file-description" title="Trei laturi AB, BC și CA, fiecare între două vârfuri ale unui triunghi"><img alt="Trei laturi AB, BC și CA, fiecare între două vârfuri ale unui triunghi" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Triangle.TrigArea.svg/120px-Triangle.TrigArea.svg.png" decoding="async" width="120" height="108" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Triangle.TrigArea.svg/180px-Triangle.TrigArea.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Triangle.TrigArea.svg/240px-Triangle.TrigArea.svg.png 2x" data-file-width="165" data-file-height="148" /></a></span></div> <div class="gallerytext">Trei laturi AB, BC și CA, fiecare între două vârfuri ale unui <a href="/wiki/Triunghi" title="Triunghi">triunghi</a></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Square_(geometry).svg" class="mw-file-description" title="Un poligon este mărginit de laturi; acest pătrat are 4 laturi"><img alt="Un poligon este mărginit de laturi; acest pătrat are 4 laturi" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Square_%28geometry%29.svg/120px-Square_%28geometry%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Square_%28geometry%29.svg/180px-Square_%28geometry%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Square_%28geometry%29.svg/240px-Square_%28geometry%29.svg.png 2x" data-file-width="120" data-file-height="120" /></a></span></div> <div class="gallerytext">Un poligon este mărginit de laturi; acest <a href="/wiki/P%C4%83trat" title="Pătrat">pătrat</a> are 4 laturi</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Hexahedron.png" class="mw-file-description" title="Într-un poliedru fiecare latură face parte din două fețe, ca la acest cub."><img alt="Într-un poliedru fiecare latură face parte din două fețe, ca la acest cub." src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Hexahedron.png/120px-Hexahedron.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Hexahedron.png/180px-Hexahedron.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Hexahedron.png/240px-Hexahedron.png 2x" data-file-width="1000" data-file-height="1000" /></a></span></div> <div class="gallerytext">Într-un poliedru fiecare latură face parte din două fețe, ca la acest <a href="/wiki/Cub" title="Cub">cub</a>.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Fi%C8%99ier:Hypercube.svg" class="mw-file-description" title="Fiecare latură face parte din trei sau mai multe fețe ale unui 4-politop, cum se vede în această proiecție a unui tesseract."><img alt="Fiecare latură face parte din trei sau mai multe fețe ale unui 4-politop, cum se vede în această proiecție a unui tesseract." src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Hypercube.svg/110px-Hypercube.svg.png" decoding="async" width="110" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Hypercube.svg/166px-Hypercube.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Hypercube.svg/221px-Hypercube.svg.png 2x" data-file-width="417" data-file-height="453" /></a></span></div> <div class="gallerytext">Fiecare latură face parte din trei sau mai multe fețe ale unui 4-politop, cum se vede în această proiecție a unui <a href="/wiki/Tesseract" title="Tesseract">tesseract</a>.</div> </li> </ul></div> <p>În <a href="/wiki/Geometrie" title="Geometrie">geometrie</a>, o <b>latură</b> este un tip special de <a href="/wiki/Segment_(geometrie)" title="Segment (geometrie)">segment</a>, care unește două <a href="/wiki/V%C3%A2rf_(geometrie)" title="Vârf (geometrie)">vârfuri</a> dintr-un <a href="/wiki/Poligon" title="Poligon">poligon</a>, <a href="/wiki/Poliedru" title="Poliedru">poliedru</a> sau <a href="/wiki/Politop" title="Politop">politop</a>.<sup id="cite_ref-z_1-0" class="reference"><a href="#cite_note-z-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Într-un poligon, o latură este un segment al frontierei.<sup id="cite_ref-M_2-0" class="reference"><a href="#cite_note-M-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Într-un poliedru, sau, mai general, într-un politop, o latură este un segment unde se întâlnesc două <a href="/wiki/Fa%C8%9B%C4%83_(geometrie)" title="Față (geometrie)">fețe</a>.<sup id="cite_ref-M_2-1" class="reference"><a href="#cite_note-M-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Un segment care unește două vârfuri trecând prin interior sau exterior nu este o latură ci o <a href="/wiki/Diagonal%C4%83" title="Diagonală">diagonală</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Numărul_de_laturi_ale_unui_poliedru"><span id="Num.C4.83rul_de_laturi_ale_unui_poliedru"></span>Numărul de laturi ale unui poliedru</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&veaction=edit&section=1" title="Modifică secțiunea: Numărul de laturi ale unui poliedru" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&action=edit&section=1" title="Edit section's source code: Numărul de laturi ale unui poliedru"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>(În limba română, pentru poliedre, și <i>doar</i> pentru poliedre, termenul pentru segmentul care unește două vârfuri este <b>muchie</b>, însă în alte contexte — politopuri — pentru coerența cu celelalte dimensiuni, se va folosi tot termenul „latură”.)</dd></dl> <p>Pe orice frontieră a unui <a href="/wiki/Poliedru_convex" class="mw-redirect" title="Poliedru convex">poliedru convex</a> este valabilă <a href="/wiki/Caracteristic%C4%83_Euler" title="Caracteristică Euler">caracteristica Euler</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi =V-L+F=2,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> <mo>=</mo> <mi>V</mi> <mo>−</mo> <mi>L</mi> <mo>+</mo> <mi>F</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi =V-L+F=2,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa1eaa90812b7d29f9c72c7c009d8d5b5b420554" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.253ex; height:2.509ex;" alt="{\displaystyle \chi =V-L+F=2,}"></span></dd></dl> <p>unde <i>V</i> este numărul vârfurilor, <i>L</i> este numărul laturilor, iar <i>F</i> este numărul fețelor. Această relație este cunoscută drept formula lui Euler pentru poliedre. Deci, numărul laturilor este egal cu numărul vârfurilor plus numărul fețelor minus 3. De exemplu, un cub are 8 vârfuri și 6 fețe, deci are 12 laturi. </p> <div class="mw-heading mw-heading2"><h2 id="Legătura_cu_fețele"><span id="Leg.C4.83tura_cu_fe.C8.9Bele"></span>Legătura cu fețele</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&veaction=edit&section=2" title="Modifică secțiunea: Legătura cu fețele" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&action=edit&section=2" title="Edit section's source code: Legătura cu fețele"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Într-un poligon, două laturi se întâlnesc în fiecare vârf; în general, <a href="/wiki/Teorema_lui_Balinski" title="Teorema lui Balinski">teorema lui Balinski</a> afirmă că în fiecare vârf al unui <a href="/wiki/Politop_convex" title="Politop convex">politop convex</a> <i>d</i>-dimensional se întâlnesc cel puțin <i>d</i> laturi.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Similar, într-un poliedru, pe fiecare latură se întâlnesc exact două fețe bidimensionale,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> în timp ce în dimensiuni superioare pe fiecare latură a unui politop se întâlnesc trei sau mai multe fețe bidimensionale. </p> <div class="mw-heading mw-heading2"><h2 id="Terminologie_alternativă"><span id="Terminologie_alternativ.C4.83"></span>Terminologie alternativă</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&veaction=edit&section=3" title="Modifică secțiunea: Terminologie alternativă" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&action=edit&section=3" title="Edit section's source code: Terminologie alternativă"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>În teoria politopurilor convexe din dimensiuni superioare, o <a href="/wiki/Fa%C8%9Bet%C4%83_(geometrie)" title="Fațetă (geometrie)">fațetă</a> sau <a href="/wiki/Fa%C8%9B%C4%83_(geometrie)" title="Față (geometrie)">față</a> a unui politop <i>d</i>-dimensional este unul din elementele (<i>d</i>−1)-dimensionale, o „muchie” este un element (<i>d</i>−2)-dimensional și un „pisc” este un element (<i>d</i>−3)-dimensional. Prin urmare, laturile unui poligon sunt fațetele sale, laturile unui poliedru convex (tridimensional) sunt muchiile sale, iar laturile unui politop 4-dimensional sunt piscurile sale.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Relația_cu_muchiile_din_grafuri"><span id="Rela.C8.9Bia_cu_muchiile_din_grafuri"></span>Relația cu muchiile din grafuri</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&veaction=edit&section=4" title="Modifică secțiunea: Relația cu muchiile din grafuri" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&action=edit&section=4" title="Edit section's source code: Relația cu muchiile din grafuri"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>În <a href="/wiki/Teoria_grafurilor" title="Teoria grafurilor">teoria grafurilor</a> o muchie este un obiect abstract care conectează două <a href="/wiki/Nod_(teoria_grafurilor)" title="Nod (teoria grafurilor)">noduri</a>, în mod diferit de laturile poligoanelor și poliedrelor, unde acestea sunt segmente. Totuși, orice poliedru poate fi reprezentat prin <a href="/wiki/N-schelet" title="N-schelet"><i>n</i>-scheletul</a> său (scheletul laturilor), care este un graf ale cărui noduri corespund vârfurilor poliedrului și ale cărui muchii corespund laturilor geometrice.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Invers, grafurile care sunt schelete ale poliedrelor tridimensionale pot fi caracterizate de <a href="/w/index.php?title=Teorema_lui_Steinitz&action=edit&redlink=1" class="new" title="Teorema lui Steinitz — pagină inexistentă">teorema lui Steinitz</a><sup><small>⁠(<a href="https://www.wikidata.org/wiki/Q7606897" class="extiw" title="d:Q7606897"><span title="teorema lui Steinitz la Wikidata">d</span></a>)</small></sup> ca fiind <a href="/wiki/Graf_planar" title="Graf planar">grafuri planare</a> <a href="/wiki/Graf_k-conex" title="Graf k-conex">de conexiuni ale k-vârfurilor</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&veaction=edit&section=5" title="Modifică secțiunea: Note" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&action=edit&section=5" title="Edit section's source code: Note"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small columns references-column-count references-column-count-2" style="-moz-column-count: 2; -webkit-column-count: 2; column-count: 2; list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-z-1"><b><a href="#cite_ref-z_1-0">^</a></b> <span class="reference-text">Ziegler, <i>Lectures…</i>, Definition 2.1, p. 51</span> </li> <li id="cite_note-M-2">^ <a href="#cite_ref-M_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-M_2-1"><sup><i><b>b</b></i></sup></a> <span class="reference-text"><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> Eric W. Weisstein, <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/PoligonEdge.html"><sup>[<i></i></sup></a><i><a href="/wiki/Wikipedia:Leg%C4%83turi_externe" title="Wikipedia:Legături externe">nefuncțională</a></i> <i>Poligon Edge</i>]], <i>MathWorld</i>, accesat 2021-01-03</span> </li> <li id="cite_note-3"><b><a href="#cite_ref-3">^</a></b> <span class="reference-text"><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <cite id="CITEREFBalinski1961" class="citation">Balinski, M. L. (<time datetime="1961">1961</time>), <a rel="nofollow" class="external text" href="http://projecteuclid.org/euclid.pjm/1103037323">„On the graph structure of convex polyhedra in <i>n</i>-space”</a>, <i>Pacific Journal of Mathematics</i>, <b>11</b> (2): 431–434, <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="plainlinks"><a rel="nofollow" class="external text" href="https://doi.org/10.2140%2Fpjm.1961.11.431">10.2140/pjm.1961.11.431</a> <span typeof="mw:File"><span title="Accesibil gratuit"><img alt="Accesibil gratuit" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span></span>, <a href="/wiki/Mathematical_Reviews" title="Mathematical Reviews">MR</a> <a rel="nofollow" class="external text" href="//www.ams.org/mathscinet-getitem?mr=0126765">0126765</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Pacific+Journal+of+Mathematics&rft.atitle=On+the+graph+structure+of+convex+polyhedra+in+n-space&rft.volume=11&rft.issue=2&rft.pages=431-434&rft.date=1961&rft_id=info%3Adoi%2F10.2140%2Fpjm.1961.11.431&rft_id=%2F%2Fwww.ams.org%2Fmathscinet-getitem%3Fmr%3D0126765&rft.aulast=Balinski&rft.aufirst=M.+L.&rft_id=http%3A%2F%2Fprojecteuclid.org%2Feuclid.pjm%2F1103037323&rfr_id=info%3Asid%2Fro.wikipedia.org%3ALatur%C4%83+%28geometrie%29" class="Z3988"><span style="display:none;"> </span></span><style data-mw-deduplicate="TemplateStyles:r16236537">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"„""”""«""»"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}</style></span> </li> <li id="cite_note-4"><b><a href="#cite_ref-4">^</a></b> <span class="reference-text"><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <cite id="CITEREFWenninger1974" class="citation">Wenninger, Magnus J. (<time datetime="1974">1974</time>), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=N8lX2T-4njIC&pg=PA1"><i>Polyhedron Models</i></a>, Cambridge University Press, p. 1, <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/9780521098595" title="Special:Referințe în cărți/9780521098595">9780521098595</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Polyhedron+Models&rft.pages=1&rft.pub=Cambridge+University+Press&rft.date=1974&rft.isbn=9780521098595&rft.aulast=Wenninger&rft.aufirst=Magnus+J.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DN8lX2T-4njIC%26pg%3DPA1&rfr_id=info%3Asid%2Fro.wikipedia.org%3ALatur%C4%83+%28geometrie%29" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537">.</span> </li> <li id="cite_note-5"><b><a href="#cite_ref-5">^</a></b> <span class="reference-text"><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <cite id="CITEREFSeidel1986" class="citation">Seidel, Raimund (<time datetime="1986">1986</time>), „Constructing higher-dimensional convex hulls at logarithmic cost per face”, <i>Proceedings of the Eighteenth Annual ACM Symposium on Theory of Computing (STOC '86)</i>, pp. 404–413, <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F12130.12172">10.1145/12130.12172</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Constructing+higher-dimensional+convex+hulls+at+logarithmic+cost+per+face&rft.btitle=Proceedings+of+the+Eighteenth+Annual+ACM+Symposium+on+Theory+of+Computing+%28STOC+%2786%29&rft.pages=404-413&rft.date=1986&rft_id=info%3Adoi%2F10.1145%2F12130.12172&rft.aulast=Seidel&rft.aufirst=Raimund&rfr_id=info%3Asid%2Fro.wikipedia.org%3ALatur%C4%83+%28geometrie%29" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537">.</span> </li> <li id="cite_note-6"><b><a href="#cite_ref-6">^</a></b> <span class="reference-text"><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <cite id="CITEREFSenechal2013" class="citation">Senechal, Marjorie (<time datetime="2013">2013</time>), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=kZtCAAAAQBAJ&pg=PA81"><i>Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination</i></a>, Springer, p. 81, <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/9780387927145" title="Special:Referințe în cărți/9780387927145">9780387927145</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Shaping+Space%3A+Exploring+Polyhedra+in+Nature%2C+Art%2C+and+the+Geometrical+Imagination&rft.pages=81&rft.pub=Springer&rft.date=2013&rft.isbn=9780387927145&rft.aulast=Senechal&rft.aufirst=Marjorie&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DkZtCAAAAQBAJ%26pg%3DPA81&rfr_id=info%3Asid%2Fro.wikipedia.org%3ALatur%C4%83+%28geometrie%29" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"></span> </li> <li id="cite_note-7"><b><a href="#cite_ref-7">^</a></b> <span class="reference-text"><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <cite id="CITEREFPisanskiRandić2000" class="citation">Pisanski, Tomaž; Randić, Milan (<time datetime="2000">2000</time>), „Bridges between geometry and graph theory”, În Gorini, Catherine A., <i>Geometry at work</i>, MAA Notes, <b>53</b>, Washington, DC: Math. Assoc. America, pp. 174–194, <a href="/wiki/Mathematical_Reviews" title="Mathematical Reviews">MR</a> <a rel="nofollow" class="external text" href="//www.ams.org/mathscinet-getitem?mr=1782654">1782654</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Bridges+between+geometry+and+graph+theory&rft.btitle=Geometry+at+work&rft.place=Washington%2C+DC&rft.series=MAA+Notes&rft.pages=174-194&rft.pub=Math.+Assoc.+America&rft.date=2000&rft_id=%2F%2Fwww.ams.org%2Fmathscinet-getitem%3Fmr%3D1782654&rft.aulast=Pisanski&rft.aufirst=Toma%C5%BE&rft.au=Randi%C4%87%2C+Milan&rfr_id=info%3Asid%2Fro.wikipedia.org%3ALatur%C4%83+%28geometrie%29" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537">. V. în special Teorema 3, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Eb6uSLa2k6IC&pg=PA176">p. 176</a></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografie">Bibliografie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&veaction=edit&section=6" title="Modifică secțiunea: Bibliografie" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&action=edit&section=6" title="Edit section's source code: Bibliografie"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <cite id="CITEREFZiegler1995" class="citation">Ziegler, Günter M. (<time datetime="1995">1995</time>), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=xd25TXSSUcgC&pg=PA51"><i>Lectures on Polytopes</i></a>, <a href="/wiki/Graduate_Texts_in_Mathematics" title="Graduate Texts in Mathematics">Graduate Texts in Mathematics</a>, <b>152</b>, Springer, <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/9780387943657" title="Special:Referințe în cărți/9780387943657">9780387943657</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lectures+on+Polytopes&rft.series=Graduate+Texts+in+Mathematics&rft.pub=Springer&rft.date=1995&rft.isbn=9780387943657&rft.aulast=Ziegler&rft.aufirst=G%C3%BCnter+M.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dxd25TXSSUcgC%26pg%3DPA51&rfr_id=info%3Asid%2Fro.wikipedia.org%3ALatur%C4%83+%28geometrie%29" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"></li></ul> <div class="mw-heading mw-heading2"><h2 id="Lectură_suplimentară"><span id="Lectur.C4.83_suplimentar.C4.83"></span>Lectură suplimentară</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&veaction=edit&section=7" title="Modifică secțiunea: Lectură suplimentară" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&action=edit&section=7" title="Edit section's source code: Lectură suplimentară"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <cite id="CITEREFMatoušek2002" class="citation">Matoušek, Jiří (<time datetime="2002">2002</time>), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=0N5RVe5lKQUC&pg=PA86"><i>Lectures in Discrete Geometry</i></a>, Graduate Texts in Mathematics, <b>212</b>, Springer, <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Special:Referin%C8%9Be_%C3%AEn_c%C4%83r%C8%9Bi/9780387953748" title="Special:Referințe în cărți/9780387953748">9780387953748</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lectures+in+Discrete+Geometry&rft.series=Graduate+Texts+in+Mathematics&rft.pub=Springer&rft.date=2002&rft.isbn=9780387953748&rft.aulast=Matou%C5%A1ek&rft.aufirst=Ji%C5%99%C3%AD&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D0N5RVe5lKQUC%26pg%3DPA86&rfr_id=info%3Asid%2Fro.wikipedia.org%3ALatur%C4%83+%28geometrie%29" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"></li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <cite id="CITEREFGrünbaum2003" class="citation">Grünbaum, Branko (<time datetime="2003">2003</time>), <i>Convex Polytopes</i>, Graduate Texts in Mathematics, <b>221</b> (ed. 2nd), Springer</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Convex+Polytopes&rft.series=Graduate+Texts+in+Mathematics&rft.edition=2nd&rft.pub=Springer&rft.date=2003&rft.aulast=Gr%C3%BCnbaum&rft.aufirst=Branko&rfr_id=info%3Asid%2Fro.wikipedia.org%3ALatur%C4%83+%28geometrie%29" class="Z3988"><span style="display:none;"> </span></span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r16236537"></li></ul> <div class="mw-heading mw-heading2"><h2 id="Legături_externe"><span id="Leg.C4.83turi_externe"></span>Legături externe</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&veaction=edit&section=8" title="Modifică secțiunea: Legături externe" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Latur%C4%83_(geometrie)&action=edit&section=8" title="Edit section's source code: Legături externe"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="noprint tright portal" style="border:solid #aaa 1px; 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font-weight: bold"><b><a href="/wiki/Portal:Matematic%C4%83" title="Portal:Matematică">Portal Matematică </a></b> </td></tr> </tbody></table></div> <ul><li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/PoligonEdge.html">Poligon Edge</a><sup>[<i><a href="/wiki/Wikipedia:Leg%C4%83turi_externe" title="Wikipedia:Legături externe">nefuncțională</a></i>]</sup>, (<a href="/wiki/Limba_rom%C3%A2n%C4%83" title="Limba română">română</a> <span lang="ro" style="font-style:italic">Latură de poligon</span>) la Mathworld</li> <li><span style="border:solid 1px #44A; background-color:#EEF; font-family:monospace; color:#008; font-size:0.9em; padding:0px 4px 2px 4px; position:relative; bottom:0.2em; cursor:help;" title="Limba engleză">en</span> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/PolyhedronEdge.html">Polyhedron Edge</a>, (<a href="/wiki/Limba_rom%C3%A2n%C4%83" title="Limba română">română</a> <span lang="ro" style="font-style:italic">Muchie de poliedru</span>) la Mathworld</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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